Metamath Proof Explorer

Theorem nelsn

Description: If a class is not equal to the class in a singleton, then it is not in the singleton. (Contributed by Glauco Siliprandi, 17-Aug-2020) (Proof shortened by BJ, 4-May-2021)

Ref Expression
Assertion nelsn A B ¬ A B


Step Hyp Ref Expression
1 elsni A B A = B
2 1 necon3ai A B ¬ A B